Stochastic Port-Hamiltonian Systems Under Information Uncertainties

Industrial circuit systems are subject to significant information uncertainties, such as noise, incomplete state measurements, unknown loads, and lumped disturbances, which can jeopardize stability and safety. This article addresses these challenges in stochastic port-Hamiltonian systems (SPHSs) through novel control strategies. A reduced-order observer, formulated via linear matrix inequalities, is developed to observe system states when complete measurements are unavailable. We prove that the observation error converges to zero both in almost sure and mean square senses. For SPHS with lumped disturbances, a disturbance observer enables feedforward compensation by observing unknown disturbances. In addition, tunable estimators are proposed to identify constant but unknown loads, with performance optimized through function selection. Furthermore, based on stochastic versions of LaSalle’s invariance principle and Barbalat’s lemma, we prove that a SPHS which is passive under constant control is also stabilizable via proportional–integral control. The efficacy of the proposed methods is demonstrated through circuit simulation examples, confirming their applicability in mitigating information uncertainties in industrial environments.